Cycles mapping node - rotation pivot
The pivot of an image will always be at the origin, which Blender defines as the bottom left.

The trick to moving the pivot is to actually move the image first, so that the point in the image that you want to be the pivot is over the bottom left (the actual pivot), then do your rotations, and then move it back where you want it.



The lighter orange area is the actual UV space (0-1), the darkened part is outside the UV space but still useful to visualize what's going on.

Notice how the first mapping node's location is negative, and the second mapping node's location is the same but positive.

0.5 is used here to place the pivot in the middle of the image, though you can use whatever values you like as long as they're the same for each mapping node, but inverse.